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      Homogenization of a mean field game system in the small noise limit

      February 26, 2016

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      Mathematics
      Analysis of PDEs
      This paper concerns the simultaneous effect of homogenization and of the small noise limit for a 2nd2^{\textrm {nd}}2nd order mean field games (MFG) system with local coupling and quadratic Hamiltonian. We show under some additional assumptions...

      Algebraic Databases

      February 10, 2016

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      Mathematics
      Computer Science
      Category Theory
      Databases
      Category Theory
      Databases
      Databases have been studied category-theoretically for decades. The database schema -- whose purpose is to arrange high-level conceptual entities -- is generally modeled as a category or sketch. The data itself, often called an instance, is...

      Isolated elliptic fixed points for smooth Hamiltonians

      February 8, 2016

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      Mathematics
      Dynamical Systems
      We construct on R2d\R^{2d}R2d, for any d≥3d \geq 3d≥3, smooth Hamiltonians having an elliptic equilibrium with an arbitrary frequency, that is not accumulated by a positive measure set of invariant tori. For d≥4d\geq 4d≥4, the Hamiltonians we construct...

      What is the absolutely continuous spectrum?

      February 4, 2016

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      Physics
      Mathematics
      Mathematical Physics
      Statistical Mechanics
      Mathematical Physics
      Quantum Physics
      Mathematical Physics
      Statistical Mechanics
      Mathematical Physics
      Quantum Physics
      We summarize (and comment on) the research program carried out in (CMP 319, 501 (2013)), (CMP 338, 347 (2015)), (CMP 344, 959 (2016), (LMP 106, 787 (2016)). This program is devoted to the characterization of the absolutely continuous spectr...

      Bayesian Dynamic Quantile Model Averaging

      February 2, 2016

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      Mathematics
      Statistics
      Statistics Theory
      Methodology
      Statistics Theory
      This article introduces a novel dynamic framework to Bayesian model averaging for time-varying parameter quantile regressions. By employing sequential Markov chain Monte Carlo, we combine empirical estimates derived from dynamically chosen ...

      Symplectic resolutions of quiver varieties

      January 30, 2016

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      Mathematics
      Algebraic Geometry
      Representation Theory
      In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic res...

      Orientations of Morse flow trees in Legendrian contact homology

      January 27, 2016

      Mathematics
      Symplectic Geometry
      Let Λ\LambdaΛ be a closed, connected, spin Legendrian submanifold of the 1-jet space of a smooth nnn-dimensional manifold. We give a coherent orientation scheme for the moduli space of rigid Morse flow trees of Λ\LambdaΛ, implying that the ...

      Fundamental Limits of Covert Communication over Classical-Quantum Channels

      January 25, 2016

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      Physics
      Computer Science
      Mathematics
      Quantum Physics
      Information Theory
      Information Theory
      Quantum Physics
      Information Theory
      Information Theory
      We investigate covert communication over general memoryless classical-quantum channels with fixed finite-size input alphabets. We show that the square root law (SRL) governs covert communication in this setting when product of nnn input sta...

      Primordial black hole formation from cosmological fluctuations

      January 23, 2016

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      Physics
      Cosmology and Nongalactic Astrophysics
      General Relativity and Quantum Cosmology
      High Energy Physics - Theory
      Cosmology and Nongalactic Astrophysics
      General Relativity and Quantum Cosmology
      High Energy Physics - Theory
      Primordial black holes (PBHs) are those which may have formed in the early Universe and affected the subsequent evolution of the Universe through their Hawking radiation and gravitational field. To constrain the early Universe from the obse...

      On the capacity functional of the infinite cluster of a Boolean model

      January 19, 2016

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      Mathematics
      Probability
      The original 2017 version of this paper, published in Ann. Appl. Probab., 27, 1678--1801, contains a major gap in the proofs. In the subsequent publication in Ann. Appl. Probab., 34, 3370--3374, 2024, we indicated how to fix this. For conve...
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